arXiv:1802.03414v1 [astro-ph.GA] 9 Feb 2018 gs(see ages to bracketed between is pened disc Galactic blurr the remains in Way, star-formation Milky of the onset into deposited a i time were the those stars i.e. assembly, these to halo compared the of earlier epoch formed the However, disc. halo Galactic the in Stars INTRODUCTION 1 ofraino h icadteselrhalo stellar the and disc the of Co-formation 3Fbur 2018 February 13 ubetm g see.g. (see l ago slightly only time populations Hubble stellar a their of bulk the formed .Belokurov V. MNRAS ⋆ ( Gyr 2009 al. et Tolstoy 2002 al. et Hansen 2016 al. et Martig 2017 al. et Kilic † 2014 ( itself Universe the as old as nearly stars host spheroidals cluster globular halo’s from ex the For that age disc. determined in the been for has as it procedures ple, same the following timated 2005 3 2 1 5 4 c eateto hsc,Uiest fSre,GidodGU2 Guildford Surrey, of University Physics, of Department etrfrCmuainlAtohsc,Faio Institut Flatiron Astrophysics, Computational 0HA for CB3 Center Cambridge, Rd, Madingley Astronomy, of Institute nttt o opttoa omlg,Dprmn fPhys of Department Cosmology, Computational for Institute eateto hsc,MWlim etrfrCsooy Ca Cosmology, for Center McWilliams Physics, of Department E-mail:[email protected] hsppri eiae otemmr fPoesrDnl Lyn Donald Professor of memory the to dedicated is paper This 00TeAuthors The 0000 h rtatmtt eihrtehsoyo h omto of formation the of history the 10-12 decipher of range to the attempt in first ages The have stars halo the field, the In ). es be can populations stellar halo’s the of times birth The ). ore&Wis2011 Weiss Jofr´e & 000 sate l 1996 al. et Oswalt 0–0 00)Pern 3Fbur 08Cmie sn MN using Compiled 2018 February 13 Preprint (0000) 000–000 , ∼ 0to 10 ∼ ,iohoemdlig(e.g. modelling isochrone ), and 8 n uloomcrnlg ( nucleocosmochronology and ) ,wiemn lr-an wrsapa ohave to appear dwarfs ultra-faint many while ), , 2007 1 ∼ , ∼ 2 3Grdpnigo ealct see.g. (see metallicity on depending Gyr 13 † ; 1Grao ae nwiedafcooling dwarf white on based ago, Gyr 11 ; ii ta.2012 al. et Kilic .Erkal D. , adnege l 2013 al. et VandenBerg ; egt ta.1998 al. et Leggett eouo ta.2007 al. et Belokurov e words: Key hal radical orbit, The disc. progenitor’s ago. massive Gyr the of 11 radialisation and dramatic 8 between i.e. formation, disc wr aelts nta,w ru,teselrdbi nt in with satellite debris a stellar by the event argue, accretion major we inconsisten Instead, is anisotropy satellites. acute dwarf observed the that deduce we 20 iiyrnecniee,i.e. considered, range licity eto oprdt h agniloe smll ailwit radial mildly amoun is (the one) anisotropy tangential orbital the the to end, ellipsoid compared [Fe/H] velocity halo’s low rection (within the the local that At the ity. demonstrate of We properties halo. kinematic lar the study we SDSS, sn ag apeo anSqec tr ih7Dmeasurem 7-D with stars Sequence Main of sample large a Using ABSTRACT o tr ih[Fe/H] with stars for < 1 ; v ¯ , aia 2012 Kalirai 3 θ awo ta.2013 al. et Haywood (kms ..Evans N.W. , ; nxe l 1999 al. et Knox e eooe al. et Peloso del ik a aais wr aais tutr oa Gro Local – structure galaxies: – dwarf galaxies: – Way Milky − ,125hAeu,NwYr,N 01,USA 10010, NY York, New Avenue, 5th 162 e, .Ms dwarf Most ). ; 1 rw tal. et Brown ) c,Uiest fDra,SuhRa,Dra H L,UK 3LE, DH1 Durham Road, South Durham, of University ics, X,UK 7XH, ). < aehap- have ngeMlo nvriy 00Fre vne Pittsburgh, Avenue, Forbes 5000 University, Mellon rnegie s than ess den-Bell range s which t 30 .The y. > the n sn ut fcsooia omi iuain fhl f halo of simulations zoom-in cosmological of suite a Using . am- see − - ; ; 1 1 − . ..Koposov S.E. , 7 3 emaueeteevle of values extreme measure we < h aatcds n h tla aocnb on in found be can halo stellar the and disc Galactic the h hoeia nihsit h yaiso h on Gala young the of by dynamics posed the into insights theoretical of properties the observational the to af pertaining concerns bias the selection by a considered by dataset the caused ing been have might metallicity and 1998 n omv necnrcobt.I peia oa coordina meta polar are spherical stars In orbits. halo supported eccentric the on not move of do is fraction and halo large stellar a undeniably, the data, in metallicity with erties e.g. (see studies 1995 Sommer-Larsen Later & Beers sample. pro stellar b chemo-kinematic their to the ought of explaining stars halo thus the eccentric, of orbits highly the collapse, the by driven ( 0yasago. years 50 As the halo. affected stellar st profoundly old younger the also of of but population shapes orbits, a con circular yielded The only nearly stars. fash not on of Galaxy instantaneous generations the nearly of subsequent a tion the in to collapsed birth then giving cloud gas Th metal-deficie configuration. inal the spherical approximately that an conclude in eccen first authors formed the the and orbits, neighborhood their Solar of the in stars of metallicity 1962 [Fe/H] hlttehptei fsrc reigo h ria prop orbital the of ordering strict of hypothesis the Whilst eccentr the between correlation claimed the that revealed ) .Bsdo h togaprn orlto ewe the between correlation apparent strong the on Based ). − M ge tal. et Eggen 1 h tla aossi smnml ttelvlof level the at minimal, is spin halo’s stellar the , vir > ⋆ 1 10 , 4 ( 10 1962 n ..Deason A.J. and M mlfidb h cino h growing the of action the by amplified ⊙ r silmntn oa ste were they as today illuminating as are ) einrhl eedpstdi a in deposited were halo inner he ihtecniuu crto of accretion continuous the with t ge tal. et Eggen rudteeoho h Galactic the of epoch the around ; vle togywt metallic- with strongly evolves anye l 1996 al. et Carney nstoyi h euto the of result the is anisotropy o h ge tal. et Eggen β ∼ fmto nterda di- radial the in motion of t 0 0kcfo h u)stel- Sun) the from kpc 10 . A123 USA 15213, PA 2 ∼ nssple by supplied ents < β < 0 ( . 1962 9 A L RAS costemetal- the Across . ( 1962 p–stars – up .Notwithstanding ). orse l 1985 al. et Norris A 5 ; T 0 hb Yoshii & Chiba E . demonstrate, ) tl l v3.0 file style X 4 However, . ge tal. et Eggen ormation, Gaia hi data, their tstars nt sorig- is e one tes perties ecome orbital ythe by yex- xy l-poor tricity trac- fect- icity and ion, ars - ; 2 Vasily A. Belokurov et al

ties may be drastically different due to the highly stochastic nature 10 10 of the stellar halo accretion (see e.g. Cooper et al. 2010). Indeed, in numerical simulations of stellar halo formation, the anisotropy 5 5 behavior differs markedly from that of the DM one. Already in the

0 0 central parts of the Galaxy, β quickly reaches ∼ 0.5 and rises fur-

Z, kpc Z, kpc ther to β ∼ 0.8 at 100 kpc, showing a much smoother monotonic -5 -5 behavior all the way to the virial radius (see e.g. Abadi et al. 2006; Sales et al. 2007; Rashkov et al. 2013; Loebman et al. 2017). -10 -10 In this Paper, we explore the behavior of the stellar halo ve-

0 5 10 15 20 25 -3 -2 -1 0 locity ellipsoid as a function of metallicity and distance above the R, kpc [Fe/H] Galactic plane. Our sample is based on the SDSS DR9 spectro- scopic dataset and consists of Main Sequence stars with distances between < 1 and ∼ 10 kpc from the Sun. The stars included Figure 1. Galacto-centric view of the SDSS-Gaia sample. Left: Logarithm in the analysis overlap widely with selections considered by sev- of the stellar density in cylindrical R, z coordinates. Right: Logarithm of stellar density in the plane of [Fe/H] and Galactic height z. Horizontal dot- eral groups previously (see Smith et al. 2009; Bond et al. 2010; ted lines give the range of heights considered in the velocity ellipsoid anal- Loebman et al. 2014; Evans et al. 2016). However, thanks to the ysis. Gaia DR1, the proper motions of these stars are now measured with an improved accuracy. Section 2 gives the details of the stellar sam- ple under consideration, as well as the model used to characterize the stellar halo behavior. The implications of our findings and the can characterize the shape of the stellar halo’s velocity ellipsoid 2 2 comparison to the numerical simulations of the stellar halo forma- σθ +σφ by one number, the anisotropy parameter: β = 1 − 2 , where tion are presented in Section 3. 2σr β = −∞ for circular orbits and β = 1 for radial ones. In the So- lar neighborhood, the halo’s velocity ellipsoid is evidently radially biased. For example, Chiba & Yoshii (1998) obtained β = 0.52 for a small sample of local halo red giants and RR Lyrae ob- 2 DATA AND MODELLING served by the Hipparcos space mission. Using the SDSS Stripe 82 2.1 Main Sequence stars in SDSS-Gaia proper motions, and thus going deeper, Smith et al. (2009) mea- sured β = 0.69 using ∼ 2, 000 nearby sub-dwarfs. Combin- We select Main Sequence stars from the SDSS DR9 spectroscopic ing the SDSS observations with the digitized photographic plate sample (Ahn et al. 2012) by using the following cuts: |b| > 10◦, −1 measurements, Bond et al. (2010) increased the stellar halo sam- Ag < 0.5 mag, σRV < 50 kms , S/N> 10, 3.5 < log(g) < 5, ple further and derived β = 0.67. For slightly larger volumes 0.2 < g − r < 0.8, 0.2 < g − i < 2, 4500 K< Teff < 8000 probed with somewhat more luminous tracers, similar values of K and 15 100 kpc, the Solar peculiar motion presented in Cos¸kunoˇglu et al. (2011). before falling again to zero around the virial radius. The picture gets The uncertainties in distance, line-of-sight velocity and proper mo- somewhat muddled when the effects of the baryons are included. tion are propagated using Monte-Carlo (MC) sampling to obtain According to Debattista et al. (2008), halo contraction due to bary- the final uncertainties on the velocity components in spherical po- onic condensation may make the DM halos slightly more radially lar coordinates. Accordingly, for each star, its Galacto-centric co- anisotropic, but overall, the changes are small and the β trends with ordinates and velocity components are the median values of the Galacto-centric distance are preserved. On the other hand, when resulting MC distribution, and the associated “error-bars” are the the Aquarius halos are re-simulated with added gas physics and Median Absolute Deviation values scaled up by a factor of 1.48. star-formation, only some galaxies retain their DM-only anisotropy To remove the obvious outliers we cull 0.1% of stars with ex- trends, while in others, the β profile flattens and stays constant cessively high speeds. Note that the (magnitude-independent and with β ∼ 0.2 throughout the galaxy (see Tissera et al. 2010). Even metallicity-independent) proper motion uncertainties are estimated though, crudely, the physics of the formation and evolution of the using equation (2) provided in Deason et al. (2017), (for further dark and the stellar halos are the same, their redshift z = 0 proper- discussion also see de Boer et al. 2018). Furthermore, neither the

MNRAS 000, 000–000 (0000) Co-formation of the Galactic disc and the stellar halo 3

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Figure 2. Behavior of the velocity components in spherical polar coordinates, namely radial vr and azimuthal vθ, for stars in the SDSS-Gaia Main Sequence sample. The dataset is divided into metallicity bins, [Fe/H], increasing from left to right and Galactic height bins, |z|, increasing from top to bottom. The size of the median velocity error for each subset is shown in the top left corner of each panel and the total number of stars in that bin can be found in the top right corner. Pixel size is 20 × 20 kms−1. The distribution of the metal-rich stars near the Galactic plane (top right corner of the panel grid) displays two distinct populations: a cold rotating one (the thick disc) and a barely rotating, markedly radially anisotropic one (the stellar halo). Moving from top to bottom, i.e. to greater heights, the Galactic disc contribution quickly diminishes. From right to left, i.e. from metal rich to metal poor, the stellar halo’s velocity ellipsoid evolves from strongly radial to significantly more isotropic. selection procedure above nor the SDSS spectroscopic targeting of all absorption lines) is expected to be small, due to i) the low scheme (with the exception of the K-giant sample not used here) spectral resolution of the SDSS, and 2) because the binary star pe- include restrictions based on the stellar kinematics. Therefore, we riod distribution peaks at 105 days (see Raghavan et al. 2010), thus believe that the sample considered here is kinematically unbiased. yielding minuscule line shifts. To understand the possible impact of Figure 1 shows the density distribution of stars in our sample. the binarity on our results, we have carried out the following sim- A strong spatial bias due to the SDSS spectroscopic selection is ple test. We have generated a mock stellar sample corresponding clearly visible in the left panel, where stars can bee seen reach- to an old (12 Gyr) metal-poor ([Fe/H]=-1) stellar population. The ing 3 < R (kpc)< 23 and |z| < 9 kpc. The right panel gives masses of the stars are drawn from the Chabrier IMF, their distances the distribution of the stellar metallicity as a function of the Galac- from ρ ∝ r−2 radial density distribution (from 0.1 to 100 kpc) and tic height. A metal-rich, i.e. [Fe/H]∼ 0 component corresponding their velocities from a Gaussian with a constant velocity disper- to the Galactic disc is apparent at |z| < 1 kpc. Curiously, a low- sion of 100 kms−1. Assuming binary fractions of 0, 0.5 and 0.9 height density enhancement is also discernible at low metallicities, and a uniform mass ratio distribution (see Raghavan et al. 2010), i.e. [Fe/H]< −1. we calculated the impact of the binaries on the measured tangential Besides the survey-induced systematics, there may exist other velocity dispersions. Reassuringly, for the substantial 50% binary observational biases that could affect the measurements reported in fraction, only a 10% lower velocity dispersion is registered. For an this work. For example, a large and non-constant fraction of unre- unrealistically high 90% binary fraction, one would underestimate solved binary objects amongst the stars considered here could in- the tangential velocity dispersion by 20%. Accordingly, we believe fluence the kinematics in the following way. The stellar distances, that our velocity dispersion measurements (see below) are largely as predicted by the equations in Ivezi´cet al. (2008) are appropriate insensitive to the presence of unresolved binary stars in the sample. for single stars. However, if instead a star is an unresolved binary, it will appear brighter at a fixed color as compared to the fiducial rela- 2.2 7D view of the local stellar halo tion. This would in turn lead to an underestimated photometric dis- tance and therefore underestimated tangential velocity. Despite the Figure 2 shows the evolution of the azimuthal, vθ , and the radial, fact that all stars considered here have spectra, most of the poten- vr, velocity components of the stellar sample defined in the previ- tial binaries would remain undetected. This is because the fraction ous subsection as a function of metallicity, [Fe/H], and height above of stars with a clear spectroscopic binary signature (i.e. doubling the Galactic disc, |z|. Note that we use the spherical polar conven-

MNRAS 000, 000–000 (0000) 4 Vasily A. Belokurov et al

[Fe/H]<-2.30 -2.30<[Fe/H]<-2.00 -2.00<[Fe/H]<-1.66 -1.66<[Fe/H]<-1.33 -1.33<[Fe/H]<-1.00

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Figure 3. Residuals (data-model) of the fit to the distributions shown in Figure 2. Dark (white) corresponds to an excess (depletion) of stars in the data compared to the model. The number of stars per pixel contributing to the highest positive (negative) residuals are shown in the right (left) corner of each panel. The Gaussian components used to describe the data are also shown: solid white for the disc, solid black for the main halo, and white dashed for the additional halo-like component. Note a clear pattern of excess-depletion-excess along the radially stretched halo component in the right hand side of the grid. The appearance of the metal-rich halo residuals clearly indicates that the observed velocity distribution is strongly non-Gaussian. Also note a small but discernible disc-like residuals in the top-left corner of the grid (corresponding to the metal-poor stars near the Galactic plane). tion in which θ is the azimuthal angle and φ is the polar angle. In stars and the complexity of the overall velocity distribution which the Figure, the metallicity of the stars considered increases from evolves quickly as a function of metallicity and Galactic |z|, we use left to right and the Galactic height grows from top to bottom. In different numbers of Gaussian components for each sub-sample. the distributions of the stars closest to the Galactic plane (top row), The two lowest metallicity bins and the highest |z| bin are always two components with different kinematic properties are clearly dis- modelled with one 3D Gaussian (according to the number of the cernible. The (thick) disc has a negligible mean radial velocity, velocity dimensions in spherical polars). For all other subsets, in −1 −1 v¯r ∼ 0 kms , and a significant rotation, v¯θ ∼ 200 kms . Much a 3x2 array in the top right corner of Figure 2 we attempt to fit hotter in terms of its velocity dispersion, especially in the r direc- three 3D Gaussian components. However, if the resulting compo- tion, is the stellar halo whose rotation v¯θ is extremely weak. As the nent contains less than 3% of the total number of stars in a given stars get progressively metal-poorer (from right to left), the rotat- sub-sample we do not report its properties. The uncertainties of the ing component fades, and disappears completely when observed at model parameters are estimated using the bootstrap method. greater heights (middle and bottom row). Note that as shown in the The results of the multi-Gaussian decomposition of the veloc- top left corner of each panel, the velocity error changes strongly ity distributions are shown in Figure 3. Here, the significant (i.e. as a function of the Galactic |z| and for the fixed |z| is approxi- containing > 3% of total stars) model components are over-plotted mately constant across the entire metallicity range. The evolution on top of the model residuals for each sub-set in the metallicity and of the error with height is driven by the dependence of the tangen- |z| space. White solid lines give the projection of the disc’s velocity tial velocity on distance and the distance error on the photometric ellipsoid, and black solid lines show the main halo component. In uncertainty. four cases, two in the top and two in the middle row, a third halo- The most notable feature of Figure 2 is the appearance of the like Gaussian (white dashed) was required to describe the data: in stellar halo velocity ellipsoid. The halo’s distribution is demon- these cases its contribution varied between 5% and 15% of the total strated to be stretched dramatically in the radial direction for stars number of stars in the bin. As displayed in the Figure, the overall in the high metallicity range, i.e. for −1.7 <[Fe/H]< −1. How- quality of the fits is good, changing from excellent at the metal- ever, at lower metallicity, it evolves rapidly to an almost spherical poor end to satisfactory at the metal-rich extreme. Most metal-rich shape. To track the behavior of the stellar halo’s velocity ellipsoid, distributions show clear over-densities of stars with high radial ve- we model the stellar distributions shown in Figure 2 with a mix- locities, both positive and negative. These high vr “lobes” are most ture of multi-variate Gaussians using the Extreme Deconvolution visible in the two right columns of the Figure. Additionally, some algorithm described in Bovy et al. (2011). Given that the number of smaller amplitude residuals are also discernible, e.g. for the stars

MNRAS 000, 000–000 (0000) Co-formation of the Galactic disc and the stellar halo 5

Dispersion Anisotropy Rotation 200 1.0 80 1<|z|<3 3<|z|<5 5<|z|<9 0.8 150 60

0.6 > θ β σ 100 40

Figure 4. Derived properties of the velocity ellipsoid of the main stellar halo component as a function of metallicity for three different distances from the Galactic plane (indicated by color). Left: Velocity dispersion along each of the three dimensions. Note that for [Fe/H]> −1.7, the radial velocity dispersion (σr, solid lines) is approximately three times larger than those in θ (dotted) and φ (dashed) dimensions. At the metal-poor end, the three velocity dispersions come much closer to each other. Middle: Velocity anisotropy β of the stellar halo. Note a sharp change in β from nearly isotropic at the low metallicity to extremely −1 radial for the chemically enriched stars. Right: Amplitude of rotation v¯θ. The spin of the metal-rich stellar halo sub-population 20 < v¯θ (kms ) < 30 is independent of the Galactic height. The amount of rotation in the metal-poor stars appears to evolve with |z|. However, as explained in the main text, this is largely the result of low but non-negligible disc contamination and over-simplified model (one Gaussian component for the two most metal-poor sub-samples). closest to the disc, in the most metal-rich bin (top right corner of in Myeong et al. (2018a) who analyze a dataset nearly identical to −1 the grid) and e.g. at vθ ∼ 150 kms for the stars with lowest that presented here and estimate the amount of flattening in each metallicity (top left corner and adjacent). of the two halo components. Thus, the recently revealed evolution Figure 4 summarizes the evolution of the individual velocity of the shape of the stellar halo with Galactocentric distance (see disperions σr,σθ and σφ (left) and the resulting orbital anisotropy e.g. Xue et al. 2015; Das et al. 2016; Iorio et al. 2017) could be in- (middle) of the stellar halo as a function of metallicity for three terpreted as a change in the contribution from each component. different Galactic height ranges. Also shown is the behavior of the Given that our stellar sample extends as far as 10 kpc above the rotation v¯θ of the main halo (right). As hinted in the Figures 2 and 3, disc plane, it may be possible to track the differences in the den- σr,σθ,σφ and β are all a strong function of the stellar metallicity. sity distribution in the metal-rich and metal-poor sub-populations. However, this dependence does not appear to be gradual. Instead, Unfortunately, this calculation is not straightforward to carry out a sharp transition in the properties of the stellar halo’s ellipsoid in view of strong (metallicity and magnitude dependent) selection can be seen at [Fe/H]∼ −1.7. For more metal-rich halo stars, the biases of the SDSS spectroscopic survey. At the zeroth order - and anisotropy is acutely radial, with β reaching values of 0.9! How- not accounting for any selection biases - we do not record any sig- ever, the halo traced by the most metal-poor stars is almost isotropic nificant changes in the fraction of stars locked in the metal-richer with 0.2 <β< 0.4. Note also that while a visual inspection of Fig- component (i.e. with −1.66 <[Fe/H]< −1) with Galactic height: ure 2 registers a noticeable swelling of the velocity ellipsoid with it remains at a level of ∼66% across all |z| studied. Galactic |z|, this effect is mostly due to an increase in the velocity error (as shown in the top left corner of each panel). The final, de- convolved velocity dispersions take each star’s velocity uncertainty 3 DISCUSSION AND CONCLUSIONS into account and show little change in the velocity ellipsoid shape as a function of |z| (see Figure 4). In terms of the halo rotation, in- This Paper uses the SDSS-Gaia proper motions and thus our dataset teresting yet more subtle trends are apparent. Stars more metal rich is nearly identical to that of Myeong et al. (2018b,a). As shown −1 than [Fe/H]∼ −1.7 show prograde spin 20 < v¯θ (kms ) < 30 by Deason et al. (2017) and de Boer et al. (2018), both random and irrespective of the height above the Galactic plane. The rotation of systematic proper motion errors in the SDSS-Gaia catalog are min- the metal-poorer stars decreases as a function of |z|, from ∼ 50 imized compared to most previously available catalogs of simi- −1 −1 kms near the plane to < 15 kms at 5 < |z|(kpc) < 9. Over- lar depth. Instead of attempting to identify a sub-sample of halo all, based on the analysis presented here, the stellar halo appears to stars, we model the entirety of the data with a mixture of multi- be describable, albeit crudely, with a super-position of two popula- variate Gaussians. This allows us to avoid any obvious selection tions with rather distinct properties. biases and extract a set of robust measurements of the stellar halo Ours is not the first claim of the existence of (at least) two velocity ellipsoid. As seen by SDSS and Gaia, the properties of distinct components of the stellar halo (see e.g. Chiba & Beers the local stellar halo are remarkable. We show that the shape of 2000; Carollo et al. 2010). If the kinematic properties are mea- the halo’s velocity ellipsoid is a strong function of stellar metal- sured locally, then it is possible to estimate the 3-D volume den- licity, where the more metal-rich portion of halo, i.e. that with sity behavior of each of the halo components (May & Binney 1986; −1.7 <[Fe/H]< −1, exhibits extreme radial anisotropy, namely Sommer-Larsen & Zhen 1990). Based on the studies above, the 0.8 <β< 0.9 (see Figure 4). Co-existing with this highly eccen- metal-richer halo component was inferred to possess a flatter (with tric and relatively metal-rich component is its metal-poor counter- respect to the Galactic vertical direction) distribution of stars. Note part with −3 <[Fe/H]< −1.7 and β ∼ 0.3. The velocity ellipsoid that a similar argument based on the virial theorem is presented evolves rapidly from mildly radial to highly radial over a very short

MNRAS 000, 000–000 (0000) 6 Vasily A. Belokurov et al metallicity range, changing β by ∼ 0.6 over 0.3 dex. The two stel- lar halo components also display slightly different rotational prop- 1.0 M<109 50 no disc 9 10 40 disc 10 10 20 of ∼ 25 kms irrespective of Galactic height z. The spin of the 0.8 −1 10 metal-poor halo evolves from ∼ 50 kms at 1 < |z|(kpc) < 3 0 , to ∼ 20 kms−1 at 5 < |z|(kpc) < 9. Note, however, that while β 0.0 0.2 0.4 0.6 0.8 1.0 satellite orbit eccentricity the stellar halo’s properties change sharply at [Fe/H]∼ −1.7, we 0.6 do not claim that the more isotropic component does not exist at higher metallicities [Fe/H]> −1.7, it is just much weaker (see 0.4 white dashed contours in Figure 3). debris anistropy Before we discuss the implications of the measurements pre- sented above for the genesis of the stellar halo, let us briefly com- 0.2 pare the properties of the velocity ellipsoid deduced here to those disc growth in the literature. Most of the recently published halo anisotropy val- 0.0 ues are close to β < 0.7 (e.g. Smith et al. 2009; Bond et al. 2010; Posti et al. 2017), significantly lower than β ∼ 0.9 reported here. 0 2 4 6 8 accretion redshift We believe, however, that there is no obvious disagreement as pre- vious estimates combine stars across the entire metallicity range and therefore represent an average over the [Fe/H]-dependent val- Figure 5. Velocity anisotropy of the stellar debris in the Solar neighbor- ues we measure. In terms of the halo spin, the amount of prograde hood (4 < R(kpc) < 25, roughly matching the range probed by the data) rotation at high |z| is consistent with the majority of both the past as a function of the progenitor’s accretion redshift for three different sub- and recent studies of the stellar halo (see e.g. Chiba & Beers 2000; halo mass ranges. Each data-point gives the median value across the suite Deason et al. 2017). of 10 simulations. The highest radial anisotropy (for the considered range of Galactocentric radii) is attained by the debris from the most massive pro- What could be the cause of the dramatic radial anisotropy reg- 10 genitors (Mvir > 10 M⊙, red line) accreted between z = 1 and z = 3, istered at high metallicity and what is the nature of the striking bi- i.e. during the disc growth phase (correspond to 8 to 11 Gyr of lookback modality in the behavior of the stellar halo presented in the previous time, grey shaded region). The error-bar on the left hand side gives an esti- section? The two currently available theories for the formation of mate of the typical scatter in an individual (redshift, mass) bin. In the inset, the stellar halo in the vicinity of the Galactic plane invoke i) accre- the black solid (grey dashed) line shows the distribution of final orbital ec- 10 tion and disruption of multiple satellites and ii) in-situ formation of centricity for the satellites with Mvir > 10 M⊙ and accretion redshift a puffed-up rotating halo via the disc heating. However, it is hard 1 0.7. could be reconciled with either of these scenarios without any mod- The presence of the disc enhances the orbital radialisation, pushing the peak of the distribution to e> . . ification. We are not aware of any in-situ halo model where i) the 0 9 resulting halo possesses highly radial anisotropy and ii) the rota- tion signal would be as low as measured here, i.e. ∼ 25 kms−1 brary of toy models of idealized merger events in an attempt to (as judged by the metal-richer subset of our halo stars). Equally provide an atlas of the halo properties corresponding to different difficult to imagine is the idea that a prolonged accretion of multi- accretion histories. They confirm the conclusions of Deason et al. ple low-mass Galactic fragments can yield such high values of β. (2013a) that massive satellites are able to sink deeper in the poten- Given that the accreted satellites should show a diversity of orbital tial well of the Galaxy due to dynamical friction, thus dominating properties, it is more natural to expect a much more isotropic ve- the inner halo of the Galaxy. Additionally, Amorisco (2017) show locity ellipsoid, perhaps similar to what we observe at low metal- that the evolution of the orbital properties of the in-falling dwarfs licities, but wildly different from that of the metal-enriched stars, depends strongly on their mass: the low-mass systems might ex- i.e. the bulk of the stellar halo near the Sun. perience some mild orbital circularisation, while the orbits of the Recently, several arguments have been put forward to sup- more massive systems tend to radialise rather strongly. Therefore, port the idea of the halo formation through a single dominant ac- for high mass-ratio events, due to the pronounced orbital radialisa- cretion event some ∼ 10 Gyr ago (see e.g. Deason et al. 2013a; tion, the resulting stellar halo possesses negligible spin at redshift Belokurov et al. 2017). In this scenario, one massive merger pro- z = 0. This is in excellent agreement with the most recent mea- vides the lion’s share of the halo stars within ∼ 30 kpc of the surement by Deason et al. (2017) and the results presented here. Galactic center. At this characteristic radius (see e.g. Deason et al. We seek to verify the above hypothesis using a suite of 2011; Sesar et al. 2011), the properties of the stellar halo appear numerical simulations which improve on those discussed in the to change dramatically thus leading Deason et al. (2013a) to argue literature so far (such as those by Bullock & Johnston 2005; that this transition scale may correspond to the last apo-centre of Amorisco 2017). We consider 10 cosmological zoom-in simula- the halo’s progenitor before disruption. The hypothesis in which a tions of the formation of the stellar halo around galaxy hosts large portion of the inner Galaxy’s halo is dominated by the stel- with masses similar to that of the Milky Way. These simulations lar debris from a massive satellite is consistent with the abundance are described in detail in Jethwa et al. (2018) and Belokurov et al. patterns of light elements in the halo. The absence of prominent se- (2017) and are run with the N-body part of GADGET-3 which quences corresponding to contributions from low-mass systems as is similar to GADGET-2 (Springel 2005). Our stellar halo reali- well as the iron abundance at the characteristic “knee” of the stellar sations (based on tagging the most bound particles in satellites; halo’s [α/Fe] distribution (see e.g. Venn et al. 2004; Tolstoy et al. De Lucia & Helmi 2008; Bailin et al. 2014) are similar to those 2009; de Boer et al. 2014) could all be explained with the (early) presented in Bullock & Johnston (2005) and Amorisco (2017) in accretion of a massive progenitor. This interpretation is also sup- the way that they do not attempt to model the gas-dynamics and the ported by the study of Amorisco (2017) who has built a large li- feedback effects. Yet they contain some of the salient features nec-

MNRAS 000, 000–000 (0000) Co-formation of the Galactic disc and the stellar halo 7 essary to understand the stellar halo emergence, such as the mass In this regard, the low-amplitude yet clearly detectable spin of the function and the accretion time of the satellite galaxies, as well as metal-rich halo component could simply be the relic of the orbital the effect of the Galactic disc on the properties of the Dark Matter angular momentum of the parent dwarf before dissolution. This in- halo and the in-falling sub-halos. In our suite, all 10 simulations terpretation also agrees with the observed constancy of the rotation are run twice, once without a disc, and once including the effects amplitude of the metal-rich halo with the height above the Galactic of a disc. The disc is represented by a parametric Miyamoto-Nagai plane. Given the range of vertical distances probed here, any signif- potential (see Miyamoto & Nagai 1975), whose mass is grown adi- icant change in the amount of rotation would imply that the scale- abatically from redshift z = 3 to z = 1, or in lookback time, from height of the halo component considered is not dissimilar to that of 11 to 8 Gyr ago. Figure 5 shows the orbital properties of the stellar the thick disc’s. This can be contrasted to the behavior of the metal- debris as observed today in the vicinity of the Sun as a function poor halo sub-population. The amount of rotation at the metal- of the accretion time for three different progenitor mass ranges. poor end is inversely proportional to the height above the plane. Clearly, the simulated redshift z = 0 halo contains a mixture of The strongest signal of > 50 kms−1 is detected near the Galac- debris with a wide range of orbital properties. However, a trend is tic plane. As the two top left panels of Figure 3 demonstrate, the discernible in which the most massive satellites (red line) contribute single-Gaussian model produces noticeable residuals at vθ ∼ 150 stars on strongly radial orbits. Moreover, the highest anisotropy val- kms−1. Given the appearance of the model residuals for the low- ues β ∼ 0.8 are recorded for the stellar debris deposited during the est height sub-sample (top left panels), we conjecture that the halo phase of the disc assembly (grey region). spin is probably an over-estimate due to the presence of a non- Such synchronicity between the epoch of the disc growth and negligible number of non-halo stars in apparent prograde rotation. the occurrence of massive accretion events is not surprising. Before Interestingly, at metallicities [Fe/H]< −1.3 we recover a small but 10 sub-halos with virial masses Mvir > 10 M⊙ can be accreted and statistically significant positive radial velocity for stars contribut- destroyed they have to have time to grow. For example, extrapolat- ing to this disc-like population. This is consistent with the analysis ing the median halo formation time as shown in Figures 4 and 5 of of Myeong et al. (2018a) who also show that the excess of rotat- −1 Giocoli et al. (2007), the most massive Milky Way satellites would ing metal-poor stars with 0 < vr(kms ) < 20 is a strong func- not have been assembled before redshift z ∼ 2. However, there tion of Galacto-centric radius. Thus, it is unlikely that this signal are additional factors that may explain the coincidence of the disc is provided by a (thick) disc alone. Instead we conjecture that this development and the peak in the β profile in Figure 5. The inset could plausibly be a combination of an extremely metal-poor disc in the top-right corner of the Figure shows the distribution of the and stars trapped in a resonance with a bar, a feature known as the 10 orbital eccentricities of the subhaloes with Mvir > 10 M⊙ ac- Hercules stream (see Dehnen 2000; Antoja et al. 2014; Hunt et al. creted at 1 0.7, in agreement with the findings of Amorisco (2017). Note ity distribution can be adequately described with a single Gaussian, however that the peak of the distribution is pushed to even higher yielding spin values comparable (or sometimes slightly lower) to values, i.e. e > 0.9 when the disc is included (solid black line). those observed at the metal-rich end. Thus, we conclude that the satellite radialisation at the high mass An alternative explanation of the strong radial anisotropy end is enhanced by the presence of the growing disc, acting to pro- observed in the stellar halo may be provided by the ideas of mote extreme values of the velocity anisotropy of the inner stellar Eggen et al. (1962), i.e. by invoking a non-adiabatic mass growth halo as observed today. which would result in an increase of orbital eccentricities in the Using the intuition informed by the numerical experiments de- halo. However, this dramatic contraction of the young Galaxy scribed above, let us return to the view of the stellar halo given would affect all stars situated in the Milky Way at that time, ir- in Figures 2 and 3. The radically radial component of the nearby respective of their metallicity. This can be contrasted with the mea- stellar halo is also the one that contains the most metal-rich halo surements reported here: at the metal-poor end, a much lower ve- stars, in agreement with the mass-metallicity relationship observed locity anisotropy is observed, 0.2 <β< 0.4. This nearly isotropic in dwarf galaxies (Kirby et al. 2013). Note however, that in the velocity ellipsoid can still be reconciled with the hypothesis of the (vr, vθ) plane, the density distribution of this sausage-like popu- collapse-induced radialisation if the metal-poor stars were either lation is not exactly Gaussian, as manifested by a pronounced ex- accreted after the prolific growth phase or stayed sufficiently far cess of stars with high positive/negative radial velocity (see Fig- away from the portions of the Galaxy undergoing rapid transforma- ure 3). We believe, however, that the black-white-black pattern of tions. However, as Figure 5 demonstrates, there may be a simpler the residuals’ distribution in the right-hand side of the Figure can be explanation of the dependence of the velocity ellipsoid on the stel- equally well explained by the lack of stars with low radial speeds. lar metallicity. According to the Figure, moderate radial anisotropy This interpretation may be more appropriate if the Sun is located appears consistent with the stellar debris contributed by the low- somewhere in the middle of a giant cloud of stars on highly ra- mass objects, irrespective of the accretion redshift. Thus, the Cos- dial orbits (with their peri-centres at small Galactic radii and the mological zoom-in simulations paint a picture in which the stellar apo-centres not far from the break radius at ∼30 kpc). Limited by halo dichotomy emerges naturally due to a correlation between the the available data, our view of the halo lacks stars near the turning orbital properties of the accreted dwarfs and their masses. points - apos and peris - where the radial motion is the slowest. We have validated this idea using the numerical simulations described above. Most importantly, given that due to the selection effect de- ACKNOWLEDGMENTS scribed above, the velocity distribution is noticeably non-Gaussian, the (already high) anisotropy value for the metal-rich component The research leading to these results has received funding from the may actually be an under-estimate. European Research Council under the European Union’s Seventh Notwithstanding the strong radialisation of the progenitor’s Framework Programme (FP/2007-2013) / ERC Grant Agreement n. orbit, it is unlikely that it would lose all of its angular momentum. 308024. A.D. is supported by a Royal Society University Research

MNRAS 000, 000–000 (0000) 8 Vasily A. Belokurov et al

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